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Chapter 0: Problem 51

Evaluate the expressions, rounding your answer to four significant digits where necessary. $$ \sqrt[3]{27 / 8} $$

Short Answer

Expert verified
The cube root of the given expression, \(\sqrt[3]{\frac{27}{8}}\), is \(\frac{3}{2}\) or 1.5 after rounding to four significant digits.

Step by step solution

01

Write the expression as a power

Write the given expression, \(\sqrt[3]{\frac{27}{8}}\), as a power by raising the fraction to the power of 1/3: \[ \left(\frac{27}{8}\right)^{\frac{1}{3}} \]
02

Evaluate the cube root

Find the cube root by raising both the numerator and denominator to the power of 1/3: \[ \frac{27^{\frac{1}{3}}}{8^{\frac{1}{3}}} \] Evaluating: \[ \frac{3}{2} \]
03

Round to four significant digits

The result obtained is already rounded to 4 significant digits, which is \(\frac{3}{2}\) or 1.5. Our final answer is: \[ \sqrt[3]{\frac{27}{8}} = 1.5 \]

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